(i) 4500
At first, We’ll resolve the given number into prime factors:
Hence,
4500 = 4 × 125 × 9
= 2 × 2 × 3 × 3 × 5 × 5 × 5
= (5 × 3 × 2) × (5 × 3 × 2) × 5
In the above factors only 5 is unpaired
So, in order to get a perfect square the given number should be divided by 5
Hence,
The number whose perfect square is the new number is as following:
= (5 × 3 × 2) × (5 × 3 × 2)
= (5 × 2 × 3) × (5 × 2 × 3)
= (5 × 2 × 3)2
= (30)2
(ii) 7776
At first, We’ll resolve the given number into prime factors:
Hence,
7776 = 32 × 243
= 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 2
= (2 × 2 × 3 × 3) × (2 × 2 × 3 × 3) × 2 × 3
In the above factors only 2 and 3 are unpaired
So, in order to get a perfect square the given number should be divided by 6
Hence,
The number whose perfect square is the new number is as following:
= (2 × 2 × 3 × 3) × (2 × 2 × 3 × 3)
= (2 × 2 × 3 × 3)2
= (36)2
(iii) 8820
At first, We’ll resolve the given number into prime factors:
Hence,
8820 = 4 × 5 × 9 × 49
= 2 × 2 × 3 × 3 × 7 × 7 × 5
= (7 × 3 × 2) × (7 × 3 × 2) × 5
In the above factors only 5 is unpaired
So, in order to get a perfect square the given number should be divided by 5
Hence,
The number whose perfect square is the new number is as following:
= (7 × 3 × 2) × (7 × 3 × 2)
= (7 × 3 × 2)2
= (42)2
(iv) 4056
At first, We’ll resolve the given number into prime factors:
Hence,
4056 = 8 × 3 × 169
= 2 × 2 × 13 × 13 × 3 × 2
= (13 × 2) × (13 × 2) × 6
In the above factors only 6 is unpaired
So, in order to get a perfect square, the given number should be divided by 6
Hence,
The number whose perfect square is the new number is as following:
= (13 × 2) × (13 × 2)
= (13 × 2)2
= (26)2
